Model predictive controllers (MPC) are in widespread use in industry to adjust manipulated variables (also known as inputs) with the goal of ensuring good performance of a set of controlled variables (also known as outputs). For example, U.S. Patent Publication No. 2005/50209714, to Rawlings et al. describes a single-input/single-output model predictive controller. The class of systems where MPC can be used to advantage is very large, and it includes chemical reactors, distillation columns, hydrocarbon crackers, entire refineries, as well as cement mills and kilns, robots, automobiles, aircraft, trains, amphibious vehicles, autonomous vehicles, gas turbines, and jet engines, among others. Additional systems of interest for which MPC can deliver appropriate automatic manipulations to ensure suitable functional performance include biological environments, encompassing, for example, bioreactors designed to produce insulin, and human organs such as the pancreas and its insulin and glucagons production processes, among many others. The systems of interest also include abstract human constructs that involve inputs and outputs that change with time, such as the stock market, financial models, manufacturing production models, scheduling networks for production and transportation, for example. These systems of interest are often referred to as the plant.
The popularity of MPC controllers stems from their ability to deliver good performance when deployed on complex systems featuring large numbers of inputs and outputs. Furthermore, the MPC controllers can satisfy constraints imposed by the user, such as ensuring that input values do not deviate from a range specified by maximum and minimum bounds. The MPC technology has established itself as the primary means of controlling industrial systems with multiple inputs and multiple outputs.
In spite of its high-value capabilities, it is well known that special measures must be taken to ensure that the MPC design makes the outputs achieve their specified set-point values at steady state without appreciable error. The error observed after all transient responses settle into approximately constant patterns, known as steady-state offset, is often magnified by the presence of disturbances affecting the plant.
A comprehensive discussion of design measures proposed for obtaining offset-free MPC performance at steady state is given in Muske, Kenneth. R. and Thomas A. Badgwell, “Disturbance Modeling for Offset-Free Linear Model Predictive Control”, Journal of Process Control Vol. 12, pp. 617-632, 2002, and in Pannocchia, Gabriele and James B. Rawlings, “Disturbance Models for Offset-Free Model-Predictive Control”, AIChE Journal, Vol. 49, No. 2, pp. 426-437, 2003.
The design measures advocated in the references mentioned in the preceding paragraph are challenging to deploy in a systematic fashion because they require including in the model used for designing the MPC Controller a dynamic representation of the disturbances that is often inconsistent with the structural form of the actual disturbances that affect the plant. Hence, the proposed disturbance representations are fictitious models adopted because, in cases of interest, they may bring about the beneficial consequence of eliminating steady-state offset. Unfortunately, different fictitious representations can cause different performance qualities during the transient period that precedes the onset of steady state. Furthermore, there are no systematic guidelines on how to specify an optimal disturbance structure. These approaches are therefore not of practical utility because the lack of systematic procedures in the control design process calls for significant investments of engineering effort to discriminate among many possible representations of disturbance dynamics.
In addition, some conventional techniques involve the inclusion of additional design variables, known as state and input targets, which are involved in the solution of a supplementary numerical optimization operation that often must be solved on line at every instant that the controller needs to make an adjustment. This optimization step increases the numerical cost of deploying the MPC algorithm, and introduces additional design complications because special cost matrices must be specified without the benefit of clear methodologies. Furthermore, no systematic guidelines are given to assist in the specification of effective values for the input target variable, an impediment to ensuring adequate transient performance without investing a significant amount of added engineering effort. It is often observed that the behavior of the model predictive controllers designed according to the suggestions given in the literature cited above behave in an unintuitive fashion, and thus the methodology lacks the robustness desirable in a mission-critical or high-performance control system. Performance degradation in the form of unacceptable steady-state offsets can also be observed when the operating conditions of the Plant change, which typically calls for a significant investment in additional engineering resources to redesign the MPC structure to effectively address needs of new environmental conditions.
Embodiments include a model predictive control design and deployment architecture described herein was conceived to address the shortcomings of conventional MPC systems and methods identified above. The model predictive control architecture described herein can deliver offset-free performance, and can be deployed in a systematic fashion. Furthermore, the numerical computational burden required by the technology can be significantly lower that of alternative conventional approaches documented in the literature. The MPC control scheme disclosed herein can be used to track, with little or no error, set points of a step, ramp, or parabolic type, and can reject measured or unmeasured state and output disturbances.